Issue |
ESAIM: COCV
Volume 11, Number 3, July 2005
|
|
---|---|---|
Page(s) | 449 - 472 | |
DOI | https://doi.org/10.1051/cocv:2005014 | |
Published online | 15 July 2005 |
The nonlinear membrane model: a Young measure and varifold formulation
1
Centre Universitaire de Médéa, Institut des Sciences de l'Ingénieur, CC 151, Quartier Ain-D'Heb, Médéa (26000), Algeria.
2
Laboratoire de Mécanique et de Génie Civil, UMR-CNRS 5508, Université Montpellier II, Case courier
048, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France.
3
ACSIOM et EMIAN, UMR-CNRS 5149, Université Montpellier 2 et CUFR de Nîmes, Case courier
051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France.
Received:
11
February
2004
We establish two new formulations of the membrane problem by working in the space of -Young measures and
-varifolds. The energy
functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The
interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences related to the classical
formulation. The second formulation moreover
accounts for concentration effects.
Mathematics Subject Classification: 74K15 / 35B05 / 49J45
Key words: Membrane / Young measures / varifolds.
© EDP Sciences, SMAI, 2005
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